Question

ND 67% 1 67% 18:00 Assigment 12020 @ a) What is the name given to the variable that is being estimated in a regression equation? [1 Mark] b) Given a regression equation ŷ = 2.35 + 6.82x, give the mean response if x = 10 [2 marks] c) Explain the strength and direction of the association between two variables, x and y, that have a correlation coefficient of -0.78. [2 marks] 8. A small business enterprise makes dresses and trousers. To make a dress requires hour of cutting and 20 minutes of stitching. To make trousers requires 15 minutes of cutting and hour of stitching. The profit on a dress is N$40 and on a pair of trousers N$50. The business operates for a maximum of 8 hours per day. Determine how many dresses and trousers should be made to maximize the profit and what the maximum profit is? [25 Marks]

Answer 1

a)

We will estimate dependent variable in the regression equation, here, independent variable is X and dependent variable is Y Cap, knowing the value of X, we can calculate Y cap value, as we have intercept and slope parameters.

b)

Given that X is 10

Then Y cap or mean response =2.35+(6.82*10)=70.55

c)

Correlation coefficient is negative means we have negative trend or X will increase and Y will decrease. Hence, we will see down trend relationship between two variable X and Y. again, coefficient value is 0.78 that is near to 80%, so, relationship between X and Y is strong. Most of the regression data will fall around the mean line.

8)

Maximize profit function Z =40*X1 +50*X2

Number of dress=X1 and Number of pair of trouser=X2

Constraints are:

30*X1+15*X2=<480

And

20*X1+30*X2=<480

X1 and X2>=0

33 39 - 27 24: 2 #s 15- 12 9 6 3 0 E 4 8 12 16 28 2 6 10 14 18 22

Point X coordinate (Xi) Y coordinate (X2) Value of the objetive function (2) O 0 0 A 0 32 1600 B 16 0 640 с 12 8 880 D 0 16 800 E 24 0 960

Hence, Number of dress=12 and Number of pair of trouser=8

Maximized profit Z=40*X1 +50*X2=40*12+50*8=880